Tropical limit for macroscopic systems in equilibrium defined as the formal
limit of Boltzmann constant k going to 0 is discussed. It is shown that such
tropical limit is well-adapted to analyse properties of systems with highly
degenerated energy levels, particularly of frustrated systems like spin ice and
spin glasses. Tropical free energy is a piecewise linear function of
temperature, tropical entropy is a piecewise constant function and the system
has energy for which tropical Gibbs' probability has maximum. Properties of
systems in the points of jump of entropy are studied. Systems with finite and
infinitely many energy levels and phenomena of limiting temperatures are
discussed.Comment: 16 pages, 6 figure